Question

If a lemon of radius r is divided into four identical parts, then what would be the total surface area of the four parts? (Given Area of a sphere = $4\pi r^2$)

• A. 2$\pi r^2$
• B. 4$\pi r^2$
• C. 6$\pi r^2$
• D. 8$\pi r^2$

Answer 1

The correct option is D 8$\pi r^2$

We know that,
Surface Area of Sphere = $4\pi r^2$
and, the Area of circle = $\pi r^2$
The cutting of the lemon leads to the creation of new surfaces for each part which must be counted while calculating the total surface area of the four identical parts.
Therefore,
Total Surface Area of the four identical parts,
A = 4 × {(Area of outer curved surface of each part) + (2 × Area of each plane surface i.e semi-circle)}
= 4 × {$\frac{4\pi r^2}{4}$ + 2 × $\frac{\pi r^2}{2}$ }
= 4 × ($\pi r^2$+$\pi r^2$)
= 4 × 2$\pi r^2$
= 8$\pi r^2$sq. units,
which is twice the surface area of a single sphere.